scholarly journals Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1547
Author(s):  
Xuefen Li ◽  
Fangfang Shen
Keyword(s):  
Dynamical System ◽  
Dynamical Behavior ◽  
Dynamical Behaviour ◽  
Equivalent System ◽  
Two Dimensional ◽  
Analysis Method ◽  
Random Parameters ◽  
Deterministic Equivalent ◽  
Stochastic Parameters ◽  
Perfect Symmetry

Because the two-dimensional coupled ecosystem has perfect symmetry, the dynamical behavior of symmetric dynamical system is discussed. The analysis of the dynamical behavior of a two-dimensional coupled ecosystem with stochastic parameters is explored in this paper. Firstly, a two-dimensional coupled ecosystem with stochastic parameters is established, it is transformed into a deterministic equivalent system by orthogonal polynomial approximation. Then, analysis of the dynamical behaviour of equivalently deterministic coupled ecosystems is performed using stability theory. At last, we analyzed the dynamical behaviour of non-trivial points by means of the mathematics analysis method and found the influence of random parameters on asymptotic stability in coupled ecosystem is prominent. The dynamical behaviour analysis results were verified by numerical simulation.

scholarly journals On The Dynamical Behavior of a Prey-Predator Model With The Effect of Periodic Forcing

2007 ◽  
Vol 4 (1) ◽  
pp. 147-157
Author(s):  
Baghdad Science Journal
Keyword(s):  
Dynamical System ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Chaotic Dynamics ◽  
Dynamical Behavior ◽  
Positive Equilibrium ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Periodic Forcing ◽  
Predator Model

The dynamical behavior of a two-dimensional continuous time dynamical system describing by a prey predator model is investigated. By means of constructing suitable Lyapunov functional, sufficient condition is derived for the global asymptotic stability of the positive equilibrium of the system. The Hopf bifurcation analysis is carried out. The numerical simulations are used to study the effect of periodic forcing in two different parameters. The results of simulations show that the model under the effects of periodic forcing in two different parameters, with or without phase difference, could exhibit chaotic dynamics for realistic and biologically feasible parametric values.

Constructing Permutations that Approximate Lebesgue Measure Preserving Dynamical Systems Under Spatial Discretization

1997 ◽  
Vol 07 (02) ◽  
pp. 401-406 ◽  
Author(s):  
P. E. Kloeden ◽  
J. Mustard
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lebesgue Measure ◽  
Discrete Time ◽  
Fast Algorithm ◽  
Dynamical Behavior ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Uniform Lattice ◽  
Discrete Time Dynamical System

A discrete-time dynamical system can sometimes display quite different dynamical behavior under spatial discretization. Systems generated by maps for which the Lebesgue measure is invariant are, however, robust in the sense that they can be approximated by permutations on a uniform lattice. A fast algorithm to construct such permutations is presented here and its implementation is illustrated with several examples of well–known one and two dimensional systems.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

Two-dimensional buoyant plumes in a uniform co-flow

2021 ◽  
Vol 932 ◽  
Author(s):  
Gary R. Hunt ◽  
Jamie P. Webb
Keyword(s):  
Theoretical Investigation ◽  
Analytical Solutions ◽  
Richardson Number ◽  
Relative Magnitude ◽  
Dynamical Behaviour ◽  
Finite Width ◽  
Two Dimensional ◽  
Buoyant Plumes ◽  
The Subject ◽  
Flow Case

The behaviour of turbulent, buoyant, planar plumes is fundamentally coupled to the environment within which they develop. The effect of a background stratification directly influences a plumes buoyancy and has been the subject of numerous studies. Conversely, the effect of an ambient co-flow, which directly influences the vertical momentum of a plume, has not previously been the subject of theoretical investigation. The governing conservation equations for the case of a uniform co-flow are derived and the local dynamical behaviour of the plume is shown to be characterised by the scaled source Richardson number and the relative magnitude of the co-flow and plume source velocities. For forced, pure and lazy plume release conditions the co-flow acts to narrow the plume and reduce both the dilution and the asymptotic Richardson number relative to the classic zero co-flow case. Analytical solutions are developed for pure plumes from line sources, and for highly forced and highly lazy releases from sources of finite width in a weak co-flow. Contrary to releases in quiescent surroundings, our solutions show that all classes of release can exhibit plume contraction and the associated necking. For entraining plumes, a dynamical invariance spatially only occurs for pure and forced releases and we derive the co-flow strengths that lead to this invariance.

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